Question: Express this quotient in scientific notation: ${\frac{5.940\times 10^{7}} {9.0\times 10^{1}}}$
Solution: Start by collecting like terms together. $= {\frac{5.940} {9.0}} \times{\frac{10^{7}} {10^{1}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.66 \times 10^{7\,-\,1}$ $= 0.66 \times 10^{6}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.66$ is the same as $6.60 \div 10$ , or $6.60 \times 10^{-1}$ $ = {6.60 \times 10^{-1}} \times 10^{6} $ $= 6.60\times 10^{5}$